American Economic Association
Quasi-Pareto Social Improvements
Author(s): Yew-Kwang Ng
Source: The American Economic Review, Vol. 74, No. 5 (Dec., 1984), pp. 1033-1050
Published by: American Economic Association
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Quasi-Pareto Social Improvements
By YEW-KWANG NG*
The Pareto criterion is widely accepted as
a sufficient condition for an improvement in
social welfare. If someone is made better off
and no one worse off, there seem to be no
acceptable grounds to reject the change.
However, most, if not all, changes in the real
world involve making some better off and
some (no matter how small the number)
worse off. Thus the Pareto criterion in itself
is of little practical use. On the other hand,
the search for a widely acceptable criterion
for (social) welfare improvements beyond
Pareto, around the 1940's, in the form of
compensation tests and the like, seems to
have encountered overwhelming objections.
As a result, little if any advance has since
been made. We still have not gone beyond
Pareto as far as a widely acceptable welfare
criterion is concerned.'
In Section I, I propose a widely acceptable
welfare criterion beyond the Pareto principle. The proposal consists in amending the
well-known Kaldor-Hicks-Scitovsky double
compensation test by requiring it to be
satisfied for each and every (usually income)
group of individuals. This amendment rids it
of its main objection on the ground of distributional considerations (for example, making the poor poorer and the rich much richer
is usually not regarded as a good change).2 It
may be thought that this amendment is too
restrictive and makes the criterion virtually
useless. Section II illustrates the wide appli*Reader in Economics, Monash University, Clayton,
Victoria, Australia 3168. I am grateful to my colleague
Ross Parish for stimulating discussion and to a referee
for helpful suggestions. I have also benefited from seminar discussions of earlier versions of Section III at
Monash (1976), Virginia Polytechnic Institute, New
York, and Yale universities (1978).
'For surveys of the debate on welfare criteria, see
Ezra Mishan (1969), John Chipman and James Moore
(1978), and my book (1979; 1983, ch. 3).
2Another objection of possible inconsistency after
repeated applications is discussed in the Appendix, part
A, and regarded as insignificant in practice and hence
not a compelling objection to a practical criterion.
cability of the criterion by using it to justify
a specific proposal for improving the allocation of water. Imperfect knowledge, administrative costs, and the diversity of individual
preferences make it impossible, in most cases,
to design a change or a policy that makes
every individual better off. But it may be
possible to design one that makes every group
better off, satisfying the criterion. Second,
since the criterion is meant as a sufficient,
not as a necessary, condition for a social
improvement, its acceptance does not prevent one from going beyond the criterion to
accept, say, changes that make the poor better off and the rich worse off. Third, when
combined with the third-best equality-incentive argument, this criterion leads to a much
more forceful principle of a dollar is a dollar
irrespective of income groups (Section III).
This provides a powerful simplification in
economic assessment (of any change, policy,
etc.) in general, and in cost-benefit analysis
in particular. It provides a formal justification for the separation of equity and efficiency considerations (see Richard Musgrave,
1969; A. C. Harberger, 1971, among others)
despite the presence of second-best factors
and other complications (Section IV).
I. A ProposedWelfareCriterionof
Tests
Group-SpecificCompensation
It is the hypothetical nature of compensation (i.e., without having to execute the actual compensation) that makes compensation
tests interesting. With actual compensation
to make everyone better off, the change becomes a Pareto improvement and no separate welfare criteria are necessary. But the
hypothetical nature also attracts two separate objections. First, both Nicholas Kaldor's criterion (1939; ability of gainers to
compensate losers) and John Hicks' criterion
(1940; inability of losers to bribe gainers to
oppose the change) may be logically inconsistent, since both a change and its reverse
1033
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1034
THE AMERICAN ECONOMIC REVIEW
(back to the original position) may satisfy
the same compensation test. Second, hypothetical compensation need not ensure a social improvement as the smaller amount (in
monetary terms) of loss by the losers may be
socially more important than the gain to the
gainers for some reason. Thus, if the poor
lose and the rich gain, the change may not be
regarded as an improvement even if it satisfies
all compensation tests. Hicks attempts to
overcome this second problem by arguing
that, with repeated application of compensation tests, " there would be a strong probability that almost all... [individuals] would be
better off after the lapse of a sufficient length
of time" (1941, p. 111). (See also Harold
Hotelling, 1938; James Buchanan and
Gordon Tullock, 1962, pp. 77-80; Harvey
Leibenstein, 1965.) While this is certainly a
very fruitful way of strengthening the compensation principle (as developed further by
A. Mitchell Polinsky, 1972), it does not
eliminate the problem completely as changes
that persistently hurt some particular group
cannot be ruled out completely, intertemporal substitution is not perfect, and the
aged cannot live much longer.
To overcome the two above problems of
compensation tests, I propose the following
two amendments. The first amendment was
made by Tibor Scitovsky (1941). Effectively,
a change must satisfy both the Kaldor and
the Hicks criteria. Apart from exceptional
cases (see my book 1979; 1983, Appendix
4A), little attention has to be paid to this
amendment. Especially for changes whose
effects are thinly spread across a large number of individuals, the differences between
?CV (the sum of compensating variations in
income across individuals) and EEV (sum of
equivalent variations) are likely to be small
in comparison to the inaccuracies arising
from difficulties in data collection. Thus if
we are certain that one of the two compensation tests is satisfied, the other is also most
certainly satisfied.3
3Due to the fact that CV and EV are measured at
given prices while compensation tests are based on
feasible compensation which may involve changes in
prices, a positive I2CV (2E V) is not necessarily equivalent to the satisfaction of the Kaldor (Hicks) criterion,
DECEMBER 1984
The second amendment is concerned with
the distributional issue. I. M. D. Little's
(1950; 1957) approach was to impose the
requirement that any distributional effect
must be favorable. This does not free Little's
criterion from the charge of logical inconsistency, as it requires only (at least) one of
the two compensation tests to be satisfied. I
have offered a defense of this aspect of the
Little criterion elsewhere (see my book, pp.
68-72; see also Kotaro Suzumura, 1980).
Even accepting this defense, the question of
how to decide whether the distributional
effects are "favorable" is still left unsolved.
To make our welfare criterion widely acceptable, the following amendment is proposed.
Instead of requiring the satisfaction of
compensation tests across all individuals, let
us require the same satisfaction within each
income group (or other group of the same
"deservingness," if income is not the only
problem). How finely income groups should
be defined is a matter of choice. On one
extreme, if all individuals affected by the
change fall within the same income group,
our criterion is equivalent to the KaldorHicks-Scitovsky criterion. On the other extreme, if an income group is defined narrowly enough such that each individual
income-earner is a distinct income "group,"
our criterion collapses into the Pareto criterion. This latter extreme is unlikely to be
relevant in practice for changes that affect a
large number of individuals. It is practically
impossible to distinguish an income-earner
of $23,451 per annum and another of $23,452
per annum. For most practical purposes, the
following classification is sufficient: the destitute, the very poor, the poor, the justbelow average, the average, the just-above
average, the rather well-to-do (usually called
as demonstrated by Robin Boadway (1974). Quoting
from my earlier book, "Nevertheless in the real economy where a certain change is small relative to GNP,
the payment of compensation is unlikely to change
prices significantly. Even if prices are changed, the effects
of the changes are likely to be negligible compared with
inaccuracies in data collection. Thus, if >CV is big
enough to overbalance data inaccuracies, we can be
quite safe in concluding that full compensation is possible" (p. 98). See also J. S. Dodgson (1977).
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VOL. 74 NO. 5
NG: QUASI-PARETO SOCIAL IMPROVEMENTS
the middle class?), the very well-to-do (upper
middle?) the rich, the very rich, and the
extremely rich. Of course, a finer classification may be used with actual income ranges
as well as supplementary conditions (number
of dependents, etc.) specified if desired.
The social marginal utility of a dollar is
taken as approximately the same across all
income-earners within a given income group.
Thus, if compensation is possible within each
income class, social welfare may be taken as
increased. (For complications arising from a
shift in income status from one group into
another, see the Appendix, part B). Some
people may be willing to go further by allowing net losses in higher income groups provided they are compensated by net gains in
lower income groups. I do not propose to
strengthen our welfare criterion in this way
because: 1) the criterion is meant as a sufficient condition for a social improvement, not
a necessary condition; 2) I want to command
as wide an acceptance as possible; 3) I have
a different method of dealing with the problem of equality (Section III below).
It may be thought that, by requiring the
satisfaction of the compensation test for each
income group, our criterion is very demanding if a fine grouping is adopted such that
very few changes can satisfy our criterion.
However, this is not the case, rather surprisingly. The next section illustrates how the
criterion may be used to sanction certain
changes. Section III combines the use of our
criterion with the third-best equality-incentive argument to arrive at the powerful conclusion of "a dollar is a dollar" (across all
income groups).
II. WaterPricing:An IllustrativeApplication
of OurWelfareCriterion
Water restrictions were introduced in
Melbourne in 1982 and continued until now
(end of 1983) in a bid to preserve the water
supply. It is natural for an economist to ask:
why is the price system not used to allocate
scarce water? That water is essential for life
is not the answer as many other things (food,
shelter, clothing, etc.) are also essential.
Moreover, a minimum amount (less than 5
1035
percent of present consumption) essential for
life can be allowed free and the excess
charged according to costs. The cost of
charging for water is also not the answer.
The "dominant opinion in the field of municipal water supply seems to be that universal
metering produces gains that are worth the
cost" (Jack Hirshleifer, J. C. de Haven, and
J. W. Millman, 1969, p. 45). Moreover,
Melbourne already has a metering system
with annual reading to charge for possible
excess water consumption. The free amount
of water consumption (free entitlement) is
proportional to the fixed charge which is in
turn proportional to the estimated property
value. But these free entitlements are such
that most households do not have to pay any
excess water bill even when consuming as
much water as desired. Thus, the bulk costs
(metering) of charging for water are incurred
without gaining the bulk benefit (incentive to
conserve water in accordance to its marginal
cost by the majority of consumers)-a most
uneconomical situation.
My suggestion for changing the present
system into a full pricing system (drastically
lowering the free entitlements) was referred
by the Water Supply Minister to the
Melbourne and Metropolitan Board of
Works (MMBW) for consideration. After a
discussion with the Director of Finance of
MMBW, I understand that one of the most
important factors they are concerned with is
the implication of the proposal on the cross
subsidization in the present system. This cross
subsidization exists because consumers of
high property values are paying high fixed
charges. Though they are entitled to proportionately more free water, they seldom
use the maximum free entitlements. The
situation is more or less as depicted in Figure
1. On average, consumers with property values higher than P consume less than their
free entitlements. Those consuming much less
than their free entitlements are thus effectively subsidizing those consuming more or
only slightly less than their free entitlements
(excess water consumption is charged at the
same rate as used in the calculation of the
free entitlement allowed by the fixed charge).
If the free entitlement and fixed charges
are reduced proportionately, those presently
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1036
THE AMERICAN ECONOMIC REVIEW
DECEMBER 1984
case. In the proposed system, his free entitlement is reduced to P1D. If he still consumes
the average amount P1B, he has to pay BD
for excess water consumption (the unit price
Proposed fixed
charge
is kept unchanged). But his fixed charge is
reduced by the same amount AC (= BD by
Existing average
construction). Hence he will be no better off
f
<
consumption
B,
and no worse off if he continues to consume
the same amount P1B. However, he is now
I
free
~~~~~~~~~~Proposed
I
~
entitlement
given the opportunity to reduce his water bill
by consuming less water. Thus, for the average consumer (those who consume the averpPi
age amount at their property values), no
is made worse off and most conconsumer
FIGURE 1
sumers are made better off by having the
opportunity to reduce their water bill. The
total revenue to MMBW would be unconsuming much less than their free entitlechanged if consumers did not take up this
ments (mainly those with high property valopportunity to save by conserving water. If
ues) will gain. Moreover, the per unit price
they did save, the amount of water conserved
for excess water may have to increase to
would be worth the reduced revenue colcompensate for the loss of fixed charges.
lected, assuming that the unit price is origiThus those presently consuming more than
nally fixed at an appropriate level.
their free entitlements (mainly those with low
Even ignoring problems of costs of changproperty values) may lose. (Only "may," not
ing to the new system, possible difficulties
" will," since all consumers gain from the
associated with making the cross subsidizamore efficient system and freedom from arbition more transparent, etc., the above protrary water restrictions.) Thus, unless the
posed change does not satisfy the Pareto
present cross subsidization is regarded as
criterion. This is so because not all conundesirable in some sense, the change is not
sumers are average consumers. For example,
necessarily desirable despite the pure efconsumers with properties valued at Pl may
ficiency gain. However, we may devise a
consume more or less than P1B (the average
system to capture the efficiency gain without
figure for these consumers). With the new
(on average) changing the cross subsidizasystem, those consuming less than the avertion. This can be done by reducing the fixed
age will gain (on top of the opportunity to
charges by proportionately less than the resave water) since their fixed charges will be
duction in free entitlements for consumers
reduced by the amount AC and their excess
with high property values.
water bills, even if they continue to consume
As illustrated in Figure 1, for example, the
the same amounts of water, will be only, say,
free entitlements can be reduced to a fraction
DE. Conversely, those consuming more than
of the existing average consumption and the
the average will lose (ignoring the gain from
fixed charges are adjusted accordingly such
the opportunity to save water). Thus, some
that any consumer who consumes the old
consumers will be made better off and some
average consumption at his property value
may be made worse off. The Pareto criterion
will pay the same total amount (fixed charge
is insufficient to sanction the proposed
plus excess water bill) as in the present syschange. However, at each property value,
tem. For example, a consumer whose propignoring the efficiency gain, the loss of some
erty is valued at P' is paying under the
consumers is exactly offset by the gain of
present system a fixed charge of P'A which
others. We may thus expect that our double
also measures his free entitlement. If he concompensation test will be satisfied for each
sumes the average amount of water P1B, he
group of consumers (one at each property
pays no excess water bill, as is typically the
Existing fixed charge
and free entitlement
Property
value
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VOL. 74 NO. 5
NG: QUASI-PA RETO SOCIAL IMPROVEMENTS
value) when the efficiency gain is taken into
account.4 Since the proposed change is unlikely to affect any consumer so severely as
to change his status in the income grouping
by more than one step (for complications
due to such changes, see the Appendix, part
B), and since consumers of the same property value may be taken as approximately
similar in terms of the rich-poor scale, our
welfare criterion is satisfied by the proposed
change discussed above.
The principle illustrated in the application
of this welfare criterion has wide applicability. Most changes affect different individuals
differently- some gain, some lose. Even if a
change is carefully designed so as to leave
some net gain to every group, some nonaverage individuals may still lose. The existence
of administrative costs, the lack of perfect
information, and/or the principle of equal
treatment for equals (consumers of the same
property value in the example above) preclude in most cases the possibility of designing a change that will make every individual better off. The use of our welfare
criterion thus provides an acceptable middle
ground between the Pareto criterion that is
almost never satisfied and the ordinary compensation principle that may make a whole
group of individuals (for example, the poor)
significantly worse off.
III. A Dollaris a DollarIrrespective
of IncomeGroup
Ignoring the differences between EV and
CV as insignificant and/or largely offsetting
for most changes (at least those with their
effects thinly spread; for a way to handle
exceptions, see my book, Appendix 4A), and
ignoring the effects on relative prices as again
insignificant and/or largely offsetting (see
my book, p. 98), we may regard the criteria
4Since the change is unlikely to affect prices by a
significant extent, we may expect that >2CV> 0, >2EV>
0, and that both the Kaldor and Hicks compensation
tests will be satisfied for each group of consumers,
assuming no noneconomic objection to the new system
as such.
1037
of ECV, EEV, and the Kaldor and Hicks
compensation tests as approximately equivalent. These criteria treat a dollar (gain or
loss) as equal to another dollar, to whomsoever it goes, the rich or the poor. The main
objection to such a principle of "a dollar is a
dollar" is the question of inequality in income distribution since many people regard
a dollar to the poor as satisfying more important needs than a dollar to the rich, and
believe that the relevant benefits or costs
should thus be valued accordingly in the
application of a welfare criterion or in costbenefit analysis. In particular, differential income (or distributional) weighting and other
preferential treatment between the rich and
the poor, as well as nonmarket allocation
(for example, time limits on metered parking
irrespective of willingness to pay) are regarded as desirable despite their efficiency
loss. These will be referred to as purely
equality-oriented preferential policies. Using
our welfare criterion of group-specific compensation tests, I show in this section that
the objective of income equality can be better achieved through income taxation. By
thus supporting the principle of a dollar is a
dollar, I make, somewhat paradoxically, my
own welfare criterion redundant. In other
words, after justifying a dollar is a dollar, the
group-specific proviso in compensation tests
need no longer be insisted on. (This paradox
is explained in Section V.)
Essentially, the objective of achieving a
more equal distribution of income is better
achieved through income taxation even if
disincentive effects are involved since purely
equality-oriented preferential policies have
efficiency costs5 as well as disincentive effects.
A rational individual without money illusion
will not only take into account the amount
of income earned, but also what he will get
from the income. If having a higher income
does not enable one to buy more parking
space but rather means that one has to pay
more for the same thing, and/or means that
50n the potential enormous efficiency costs of the
application of distributional weights, see Harberger
(1978).
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1038
THE AMERICAN ECONOMIC REVIEW
projects in his favor are less likely to be
undertaken, then the extra income will be
worth less than it otherwise would be. It is as
though the income tax rate has increased.
The same degree of disincentive will apply in
both cases unless income is valued not so
much for its purchasing power but mainly as
a status symbol. However, among those people for whom status considerations are important, it is more likely that the pre-tax
rather than the post-tax income will be used
as an indication. Hence the same degree of
incentive still applies.
In an ideal first-best world where costless
and neutral lump sum transfers (fixed according to potential rather than actual income) are feasible, it can easily be seen that
a dollar is a dollar. A dollar must be treated
as a dollar to maximize efficiency, and any
desired level of equality can be achieved by
lump sum transfers. But the real world is not
first best as lump sum taxes on potential
incomes are not feasible. Actual redistributive policies may take the form of (i)
measures that improve both efficiency and
equality such as the dismantling of artificial
barriers to the equality of opportunity, (ii)
progressive income taxation, and (iii) purely
equality-oriented preferential policies. Ideally, of course, all of type (i) measures should
be adopted. But usually, after all feasible
measures of that type have been used, equality is still not regarded as sufficiently attained. Hence, both types (ii) and (iii) are
also used. The inferiority of the purely equality-oriented preferential policies may be
gauged by the following proposition.
PROPOSITION 1: For any alternative (designated A) using a system (designated a) of
purely equality-orientedpreferential treatment
between the rich and the poor, there exists
another alternative, B, which does not use
preferential treatment, that makes no one
worse off, achieves the same degree of equality
(of real income, or utility) and raises more
government revenue, which could be used to
make everyone better off.
Note that this proposition is applicable
even in the case where the preferential treatment just happens to be consistent with sec-
DECEMBER 1984
ond-best efficiency considerations. Because,
alternative B, which does not incorporate
purely equality-oriented preferential policies,
but, instead, uses system b, designed for
efficiency purposes only, would already,
within that system b, incorporate the
second-best efficiency considerations with
which system a just happens to be consistent. In other words, the principle of a
dollar is a dollar does not preclude adjustments based on some efficiency considerations such as externalities, second best, etc.
But it excludes the purely equality-oriented
policies used in practice.
However, the existence of alternative B
does not necessarily mean that it can be
identified and implemented. If system a is
designed to take account of second-best
considerations, then system b can also be so
designed. But system a may only be consistent with second-best considerations by
chance rather than by design. In addition,
the informational costs of designing a system
consistent with the second-best considerations may be prohibitive.6 Then we may not
be able to identify system b. Thus, while
alternative B may exist, it may not be feasible to implement. Thus, if we wish to
strengthen Proposition 1 to be one about the
existence of a feasible superior alternative B,
it would apply only in a probabilistic sense.
That it (the strengthened proposition) still
applies in a probabilistic sense is due to the
theory of third best. Just as it may be consistent with second-best considerations, system a may also be opposite to the requirement of second best. The theory of third best
(see my 1977 article) can then be used to
show that -the expected gain is negative.
Hence, as far as the second-best consideration is concerned, the use of system a involves negative expected gains. For simplic-
6Second-best taxation-pricing rules are typically very
complicated, even if only the efficiency consideration is
taken into account. For the current literature on optimal
taxation, see James Mirrlees (1976, 1981); Agnar Sandmo
(1976). Conditions making second-best considerations
ineffective are rather stringent, for example, separability
in the utility function (see Anthony Atkinson and Joseph
Stiglitz, 1976; compare Theodore Bergstrom and Richard
Cornes, 1983).
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VOL. 74 NO. 5
1039
NG: QUASI-PARETO SOCIA L IMPROVEMENTS
ity, we may thus assume that system a is
neutral with respect to second-best considerations. (This, in fact, gives it an advantage.)
Proposition 1 is established in the Appendix, part C, under the usual assumption
that individuals have identical preferences
but different abilities. Since preferences do
differ in practice, it may thus not be actually
possible to make a Pareto improvement upon
a system using purely equality-oriented preferential policies. We would then have to
work with average individuals and construct
an alternative that makes these average individuals (one at each income level) better off.
Some nonaverage individuals would be made
better off and some worse off. In principle,
compensation may be effected to make no
one worse off. But this is not practicable.
However, while not all individuals can be
made better off in practice, each income
group could be made better off in the sense
that overcompensation is hypothetically possible at each income group. Thus, while the
Pareto criterion is not satisfied by the change,
my welfare criterion of group-specific compensation test is. Thus this welfare criterion,
when combined with the third-best equalityincentive argument, leads to the conclusion
of a dollar is a dollar.
In itself, my argument does not preclude
the joint treatment of equity and efficiency
issues due to the second-best consideration
(for example, see Dieter Bbs, 1984). But such
a sophisticated optimization procedure usually involves prohibitive informational and
administrative costs (see my 1977 article),
and is also probably politically infeasible as
it may involve prices, taxes, etc. favoring the
rich and against the poor in some (probably
half of all) sectors. As far as I know, all
preferential policies in the real world are
purely equality oriented. In combination with
this practical consideration, my. argument
also justifies the complete separation of
equity and efficiency considerations.
Let us illustrate the argument with a utility
possibility map. In Figure 2, Up and UR
represent the levels of utility of two (groups
of) individuals in the society. Starting from
the initial position D on the utility possibility curve I, consider a project (or any change)
that involves a negative aggregate net benefit
H*
\I,
\w
.
\'
\
p
~~~~~~~~UP
2
FIGUREi
(the possibility curve moves inward to II),
and a more equal distribution at point F. If
the welfare contour7 W through F passes
above D, it appears that the change is desirable. Income weighting in cost-benefit analysis that sanctions such changes seems
justified. However, to achieve the degree of
equality represented by point F, it would be
better to do so by income taxation, travelling
along curve I from D to E. It is true that
income taxation has disincentive effects and
thus the point E is not sustainable. The
disincentive effect will lead to a contraction
of the utility possibility curve I inwards (not
drawn) to pass through, say, point G. In
other words, we cannot in fact travel along
the utility possibility curve I, but have to
travel along the utility feasibility curve I' in
redistribution through income taxation. As
drawn, G is inferior to F. But what is not
commonly recognized is that point F is also
not sustainable. If redistribution through income taxation from D to E will lead to the
7Murray Kemp and 1 (1976, 1977, 1982) show that a
Bergson-Samuelson social welfare function (SWF) that
is Paretian and based only on individual ordinal preferences does not exist for any given fixed set of individual
preferences drawn from a wide domain. But we need not
confine ourselves to ordinal preferences. In fact, I have
shown elsewhere (1975) that a SWF must be an unweighted sum of individual cardinal utilities, if certain
reasonable premises are accepted.
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1040
THE AMERICAN ECONOMIC REVIEW
contraction of the utility possibility curve,
so will redistribution through cost-benefit
weighting from D to F. Abstracting from
second-best considerations, II will contract
by a roughly similar extent as I does. Hence,
instead of point F, we will end up with H
which is inferior to G. In the presence of
second-best factors, we are uncertain as
to which point we will end up with, but
the expected average is somewhat below
point H.
IV. Some Complications
In this section, I discuss factors that may
render my general argument for a dollar is a
dollar in Section III inapplicable. I show that
while these considerations qualify my conclusion, the main thrust of the central argument is not much affected.
A. Political Constraintson
RedistributionthroughTaxation
It is argued above that, instead of using
weighting, quotas, or other kinds of preferential treatment to achieve the objective of
equality (not as second-best correctives), it is
better to adopt a more progressive income
tax schedule. What if the taxation system
cannot be changed to the desired structure
due to political constraints? If it is true that
we can't change the taxation system but we
can effect redistribution by other means, my
conclusion may have to be qualified accordingly, though there is still the ethical question of the desirability of doing good by
stealth. Yet, why should the political constraint act only to prevent redistribution
though taxation and not redistribution by
other means? Maybe because the voters are
rather irrational. I suspect, however, that on
this issue, voters are very rational and practical. The upper and middle ciasses will not
only vote a government out of office for
carrying out drastic changes in taxation but
also for carrying out other drastic redistributive measures. Especially in the long run, the
forces that operate to prevent redistribution
through taxation will also operate to prevent
redistribution by other means. If we are
thinking in terms of a distributional equi-
DECEMBER 1984
librium, the distribution should be considered not in terms of money income but in
terms of real income. Naturally, if the rich
are penalized in other ways they will have
less tolerance as regards the progressiveness
of taxation. For example, had Australia been
operating closer to the principle of a dollar is
a dollar in the past, the reduction in the
progressiveness of its income tax schedule
undertaken in 1978 would probably not have
been required. Both the rich and the poor
would probably have been better off.
It is true that actual political decisions are
affected by a host of factors and not just by
an impartial consideration of a balance between equality and efficiency. However,
equality and efficiency are important considerations and the fact that preferential treatment is an inefficient tool to achieve equality
and efficiency has to be pointed out.
B. TransactionCosts
My analysis has been based on the assumption that the additional transaction costs
associated with redistribution through more
progressive income taxation are not higher
than the transaction costs of its alternatives.
Apart from the disincentive effect (which has
been taken into account and is not subsumed
under transaction costs), the costs associated
with income taxation seem to fall mainly
under 1) costs of administration on the parts
of both the taxpayers and the collectors, 2)
costs involved in tax evasion and enforcement, and 3) costs of tax lobby activities and
the like. It is recognized that all of these
forms of costs are substantial. But the relevant amounts are not total costs, only marginal costs. For good or for bad, income
taxation will be with us in the foreseeable
future. The incremental costs of administration of a more progressive tax system seem
trivial. The costs of a change from one system to another may not be trivial, but will
probably not be substantial. However, at
least in the long run, the relevant comparison
is the cost of administering two alternative
systems, the difference between which is
probably quite negligible. A more progressive tax system may however involve higher
costs in encouraging more evasion and more
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VOL. 74 NO. 5
NG: QUASI-PARETO SOCIAL IMPROVEMENTS
lobby activities. But the increase in progressiveness is in lieu of some system of preferential treatment which itself is a subject of
evasion and lobbying. While this is a subject
where a precise conclusion can hardly be
expected, it does not seem probable that
costs involved in the latter (i.e., preferential
treatment) will be much lower than costs
involved in the former (i.e., a more progressive tax system). On the other hand, the costs
of administering a pure taxation system are
almost certainly significantly lower than those
of administering a system of taxation combined with preferential treatment in government expenditure. Hence, consideration of
transaction costs seems to strengthen, not
weaken, my central conclusion.
There may be specific cases whereby the
use of an apparently "preferential" policy
may be superior to making the income tax
more progressive because of significantly
lower transaction (evasion, lobbying, and administrative) costs of the former. But such a
policy is justified on its efficiency consideration of lower transaction costs (relative to
income taxation) and cannot be justified on
the purely equality consideration advanced
by egalitarian lobbyists.
C. Ignorance of Benefit Distribution
My argument is based on the assumption
that individuals know the distribution of costs
and benefits in government expenditure
across income groups, or the details of preferential treatment, so that the incentives are
the same as an equivalent pure income taxation system. In practice, this knowledge is
unlikely to be perfect. On the other hand,
most individuals do know the scale of
income taxation. Does this asymmetrical
knowledge mean that the disincentive effects
of income taxation are more severQthan an
equivalent preferential expenditure system,
as, in effect, argued by Martin Feldstein
(1974, p. 152)?
In the absence of perfect knowledge, an
individual has to base his choice on his
estimates. From the fraction of knowledge he
possesses, it seems that he is as likely to
overestimate as to underestimate the degree
of progressiveness implied in a given pref-
1041
erential expenditure system, depending on
the psychology of the individual in question.
Hence, on the whole, the degree of incentives
is likely to be similar between the preferential expenditure system and the pure income taxation system.
D. RedistributiveEffects of the
Project Itself
I have argued that a dollar should be
treated as a dollar irrespective of whether it
accrues to the poor or to the rich. But this
argument does not show that a billion dollars is always equal to a billion dollars. This
point can be seen clearly by considering a
simple example. Consider two alternative
projects: project M will increase the incomes
(after allowing for cost share) of one million
individuals by $10 thousand each, and project N will increase the income of one single
random individual by $10 billion. Ruling out
costless lump sum transfers (that would make
us indifferent between the two projects), it is
clear that project M will be preferred to
project N by all social welfare functions
egalitarian in incomes. This preference is not
based on valuing a marginal dollar to the
rich as lower than a marginal dollar to the
poor. Rather, it is based on treating the first
dollar as more valuable than the 10 billionth
dollar, whomever they go to. (Due to diminishing marginal utility or risk aversion,
the same person typically regards the loss of
$10 thousand as more significant in utility
terms than the gain of $10 thousand, and the
gain of $10 billion as less than a million
times the gain of $10 thousand.) Hence, the
equality-incentive argument I use above does
not apply here. However, the equality-incentive argument can be used to dispel the possible belief that, since a project that itself
creates inequality is inferior to one with the
same aggregate net benefits but which does
not create inequality, a project that creates
equality must be preferable to one with the
same aggregate net benefit but distributionally neutral. Consider a third project 0 that
will yield the same aggregate net benefits of
$10 billion but be distributed across the
economy in such a way that the poor will
have much higher benefits and the rich have
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1042
THE AMERICAN ECONOMIC REVIEW
DECEMBER 1984
negative benefits. While this may seem to be
a good thing in itself, the incentive argument
will show that project 0 is in fact inferior to
project M. If project 0 were to happen as a
natural event, it would be preferable. But if
it is chosen instead of project M, it will
produce disincentive effects.
From the above, it may be said that, for
projects whose redistributive effects are marginal, one can simply choose in terms of
aggregate net benefits; for projects whose
redistributive effects are significant, we
should prefer the one with less redistributive
effects, given the same aggregate net benefits.
This seems to lend support to the concept of
a conservative social welfare function discussed by W. M. Corden (1974, p. 107).
may be in very short supply. In principle, we
could impose appropriately higher taxes on
the rich and those who happen to own the
goods in short supply and pay subsidies to
the poor and the victims of the disaster.
Then the policy of a dollar is a dollar could
still be best. However, due to time lags,
imperfect information, and the like, it may
be practically infeasible to effect the required
changes in taxes/subsidies in time. Rationing of basic necessities such as medical supplies (which also involves external economies) may then be the best practical solution.
However, the possible desirability of violating the principle of a dollar is a dollar in
such emergencies does not mean that the
same is true for normal times.
E. Preferencefor Working
G. Nonincome Indices for Preferential
Treatment
If an individual prefers to have his income
by earning it instead of receiving it as a
transfer welfare payment, then a cost-benefit
analysis that does not take this preference
into account may be misleading. This has
been emphasized by M. L. Skolnik (1970).
This kind of complication can be taken care
of by appropriate shadow pricing. For example, in the particular case considered here,
the main difference is the possible preference
of an individual for earning his income instead of receiving some kind of dole money.
This can largely be taken care of by putting
an appropriate shadow price on employment. For a single person without dependents, his income from a low-paid job is
likely to be sufficient to preclude him from
receiving a subsidy. All that is needed is a
low or zero income tax, so he will not have to
suffer the feeling of being.on the dole. For
families with dependents, the subsidy can
be effected in the form of, say, substantial
child-endowment payments differentiated according to income levels. A fixed child-endowment is used in Australia with no one
feeling ashamed of receiving it and the introduction of differentiation is unlikely to
change this substantially.
F. UnexpectedEmergencies
In times of unexpected emergencies such
as earthquakes, wars, etc., certain necessities
My analysis concentrates on the use of
income as the index for preferential treatment and redistributive taxation. But surely
income is an imperfect measure of "deservingness," and nonincome variables such
as health and age status are likely to enter
distributional objectives. In particular, the
use of age as an index for preferential treatment will create few, if any, disincentive
effects, since one cannot change one's age.
However, we can similarly use age as an
index for the purpose of tax-subsidy. The
purpose of giving assistance to the aged, for
example, can be achieved without the additional efficiency costs of, say, giving free milk
as some may not wish to drink milk. (Subsidized milk to schoolchildren may, however,
be justified on the efficiency ground of merit
wants; on merit wants as a possible efficiency
ground, see my book, Section 1OA.3). The
consideration of nonincome factors does suggest that a single tax based on incomes only
may not be sufficient; the tax-subsidy system
may have to take nonincome factors into
account.8
8 For example, consider the argument of William
Baumol and Dietrich Fischer (1979) that the use of
discrimination in wage rate is much more efficient (less
output foregone) than nondiscriminatory taxation in
achieving equality. This is based on the detailed knowl-
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VOL. 74 NO. 5
NG: QUASI-PA RETO SOCIAL IMPRO VEMENTS
A related problem of using income as the
basis for taxation is that measured income
may be a poor indicator of actual earning
potential due to savings, risk bearing, etc.
Thus, persons of the same earning potential
may be taxed more if they are more willing
to bear risk, to save, etc. However, this imperfection applies also to the use of measured income for the purpose of preferential
treatment and hence does not affect my argument. In general, to the extent that a better
index is available for use as a basis of preferential treatment, it can also be used for the
tax-subsidy purpose. Unless there are asymmetrical transaction costs (see Part B above),
no qualification to my central argument is
necessary.
From the discussion above, it may be concluded that none of the complications seem
to change my central argument significantly.
V. ConcludingRemarks
Changes satisfying my proposed welfare
criterion may be called quasi-Pareto social
improvements as all relevant (usually income) groups of individuals are made better
off in the sense of fulfilling the KaldorHicks-Scitovsky double compensation test
within each group. It is also only quasi Pareto
in the sense that repeated applications of the
Kaldor-Hicks-Scitovsky criterion may lead
to cyclicity and Pareto inferiority (Appendix,
part A). This is due to the necessary approximate nature of all objective measures of
subjective welfare changes. But the discrepancies are likely to be overwhelmed by
inaccuracies in data collection for changes
with effects thinly spread across a large number of individuals. If we are quite certain of
edge of individual input supply functions that they
recognize to be not available. But they suggest that some
rough discrimination between broad groups of income
earners such as doctors vs. ditch diggers may yet be
feasible. But if such a discrimination of supplementing
"wage rates for the one and limit[ing] wages for the
other" (p. 522) is feasible, there is little reason to expect
that it is not feasible to have higher income tax rates for
doctors and lower for ditch diggers.
1043
the fulfillment of our criterion despite data
inaccuracies, Pareto inferiority and inconsistency will almost certainly be absent. One
or two possible exceptions may be regarded
as an unavoidable cost of using a generally
good rule in practice (Appendix, part A).
When combined with the third-best equality-incentive argument, my criterion leads to
the forceful conclusion of a dollar is a dollar
irrespective of income groups. This conclusion seems to make the criterion itself redundant. The apparent paradox is easily explained. A dollar is a dollar is evaluated
prior to disincentive effects while my welfare
criterion is applied to the final outcome
inclusive of any disincentive effects. But the
principle of a dollar is a dollar does provide
a powerful simplification in economic assessment of any policy, change, etc. in general,
and in cost-benefit analysis in particular. We
may assess on pure efficiency considerations
unless certain specific preferential policies
may be justified on grounds of asymmetrical
transaction costs or asymmetrical political
feasibility, or the like (Section IV). Pure
equality considerations do not provide adequate justification for preferential treatment
between the rich and the poor, or for a
departure from a dollar is a dollar.
Consider again the water pricing example
of Section II. Unless some specific argument
(on top of equality) can be advanced for
cross subsidization, it is better to go further
than the proposal of Section II which maintains the present cross subsidization. It is
better to have a straight dollar-for-dollar
pricing system without cross subsidization.
One possible argument for cross subsidization is the infeasibility of making the income
tax system more progressive to compensate
for the withdrawal of cross subsidization.
This is quite likely true in the short run, but
not in the long run (Section IV). Another
possible argument is that it may be more
difficult to avoid paying the cross subsidies
attached to properties than to avoid paying
income taxes. If this is true, it is still better to
have a property tax than attaching the tax to
unused water entitlements with the efficiency
loss of discouraging water conservation. If
this is politically infeasible for some reason,
the proposal of Section II based on my
welfare criterion may then be considered.
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DECEMBER 1984
THE AMERICAN ECONOMIC RE VIEW
1044
APPENDIX
uK
A. The Acceptabilityof the
Kaldor-Hicks-ScitovskyCriterionin
the Absence of Distributional Considerations
Here I provide an argument in favor of
accepting the Kaldor-Hicks-Scitovsky criterion, in the absence of distributional consideration, as a practical criterion for general
economic application, despite the acknowledged possibility of cyclicity after repeated
usage.
Even abstracting away distributional
considerations (or other grounds for differentiating "deservingness"), the Kaldor-HicksScitovsky criterion (which requires the satisfaction of both the Kaldor and Hicks
compensation tests) is not an ideal sufficient
condition for a social improvement. This is
so since a logical contradiction is possible
after repeated applications of the criterion
(W. M. Gorman, 1955; John Chipman and
James Moore, Section 3; my book, p. 66). As
illustrated in the utility space of Figure 3
(where the curves are utility possibility
curves), the changes from ql to q2, q2 to q3,
q3 to q4, and q4 back to ql all satisfy the
criterion. Moreover, q4 is in fact Pareto inferior to ql. Thus the criterion is not only
logically inconsistent, but can lead to a
Pareto-inferior situation.
The possible cyclicity and Pareto inconsistency of the Kaldor-Hicks-Scitovsky criterion illustrates the difficulty of making social
welfare judgments without interpersonal
comparison of individual cardinal utilities.
In fact, I have established elsewhere (1982,
Proposition 4) that, given a sufficiently wide
domain (a condition less demanding than
Universal Domain and satisfying conventional "economic" assumptions of self interest, nonsatiation, etc.), there exists no
non-cardinalistic ranking rule yielding consistent ordering of social states satisfying
anonymity and the Pareto principle. A noncardinalistic ranking rule is a rule specifying
social ranking of pairs of social states based
on individual rankings (but not on preference intensities) of the respective pairs and
(possibly) on some (but not all) objective
characteristics of the social states. The
44
q
,
u
0
FIGURE 3
Kaldor-Hicks-Scitovsky criterion is in fact
more than a non-cardinalistic ranking rule as
it effectively uses the amount of compensation required and the willingness to pay as
indirect measures of subjective preference intensities. But since these indirect measures
are not perfect in their correspondence with
subjective preferences, inconsistencies may
arise. This difficulty is present for all nonsubjective measures of welfare. Since the relation between units of any external yardstick
of welfare such as money and internal (subjective) units of welfare is in general not a
constant (making intersections of utility possibility curves as in Figure 3 possible), such
objective measures can be, by their very nature, no more than an approximate measure
of welfare, even abstracting from the problem of inaccuracies in practical data collection. If we recognize the necessity for this
approximate nature, the possibility of inconsistency (as well as such problems as
path-dependency in consumers' surplus measurement) becomes acceptable unless the
discrepancies involved are substantial and
frequent. For general application in judging
the desirability of economic policies with
widely and thinly spread costs and benefits,
the discrepancies involved are likely to be
small and largely offsetting to each other.
Thus, if the satisfaction of the Kaldor-Hicks-
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VOL. 74 NO. 5
NG: QUASI-PARETO SOCIAL IMPROVEMENTS
Scitovsky criterion is fairly certain despite
inaccuracies in data collection, we can be
quite sure that the problem created by the
approximate nature of our measurement will
be overwhelmed. One or two odd cases of
inconsistencies may still remain, but that can
be regarded as an unavoidable cost of using
a generally desirable rule. For example, the
rule that motorists must stop at red traffic
lights is certainly desirable as it prevents
accidents and congestion, but it also creates
some unnecessary waiting time. It is Pareto
inferior for someone to wait for a green light
when no one is crossing the intersection from
any direction. But it is impractical to allow
such Pareto improvements of crossing red
lights without creating dangerous accidents.
Similarly, before it is practicable to use some
direct measurement of subjective welfares,9
we have to make do with imperfect substitutes usually in some form of willingness
to pay. Recognizing the necessary approximate nature of such measures, the possibility
of inconsistency is not a compelling objection. The use of the Kaldor-Hicks-Scitovsky
criterion, when distributional considerations
have been dealt with as suggested in Section
I, can thus be justified.
B. Dealing with Changes in
Income-GroupStatus
In Section I, a welfare criterion (or a sufficient condition for a social improvement) is
proposed that requires the satisfaction of the
Kaldor-Hicks-Scitovsky (double) compensation test for each income group. A problem
arises when some persons in an income group
are made so much better off or worse off as
to change their status into different income
groups. For example, if a change affects the
income levels of the poor by making most of
the poor poorer and making a few rich such
that compensation is possible, one may not
wish to regard such a change as socially
desirable. My compensation test will work
9Such as the psychological measurement based on
just noticeable differences; see my article (1975) on such
a measurement and ways to overcome practical difficulties.
1045
best if no such changes of income status take
place. But since a person on the top (bottom)
of an income group need only to be made a
little richer (poorer) to change his status, a
change in status by not more than one step
may be regarded as acceptable such that he
can be included in his original income group
for the purpose of compensation test. If the
social marginal utility of a dollar is regarded
as approximately equal for all individuals in
the same income group, they do not differ by
too much for neighboring income groups.
For persons who jump income groups by
more than one step, the following method of
using my compensation test is suggested. One
who jumps up the scale from income group
G to G + A, where A is a positive integer
larger than one, may be included in his original income group (G) for testing compensation provided his gain is (hypothetically) reduced to an amount making him no higher
than the top of the income group G + 1. In
other words, his gain in income above this
amount is disregarded for the purpose of the
compensation test. To be conservative, we
may insist that no one be made to jump
down the income groups by more than one
step. Alternatively, we may require that if
such a downward jumping occurs, the person
involved should be included in his new income group for the purpose of the compensation test. If we adopt the latter alternative, it is consistent to allow the following.
For a person who jumps upward by more
than one step, if his original income group
already satisfies the compensation test without including him, his gain may be included,
if needed, in the compensation test of the
income group he moves into.
C. A Dollar is a Dollar:
Proof of Proposition1
To establish Proposition 1 in Section III,
let us adopt the following simplifying assumptions: 1) there is no political constraint
on redistribution through taxation; 2) the
administrative costs of the pure taxation system are no higher than its alternative, for
any same degree of equality attained; 3) all
individuals know the relevant taxation scale,
details of government expenditure, etc.; 4)
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THE AMERICAN ECONOMIC RE VIEW
1046
DECEMBER 1984
Post-tax
D
income
I;
<13>:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
E,
_ _ _ __ _ _ _
I
0
CI
_ __ _ _ __ _ _ _
_I__
_
P re-ta x
____
C2
C3
income
FIGURE 4
there are no money illusion or similar "irrational" preferences. In Section IV, we see
that the relaxation of these assumptions does
not affect the argument significantly.
Let us define a system of perfect preferential treatment as one that involves a degree
of preferential treatment that is monotonically decreasing in incomes. Initially, I shall
establish the proposition by assuming, first,
that system a is perfect, and second, that
individuals have the same utility function
between income and leisure (but may have
different earning abilities).
Consider Figure 4 where curve a represents a given income tax schedule relating
post-tax to pre-tax income levels. For example, a person earning OC3(= C3D) will be
taxed DE3 and left with E3C3as his post-tax
income. Each person has a given incomeearning ability. Subject to this earning ability, each person may choose. different levels
of pre-tax income by varying his hours and
intensity of work. His choice depends, of
course, on his subjective preference (with
respect to leisure, consumption, and the preferential system), the tax schedule, and the
system of preferential treatment. Let alternative A be the tax schedule a and a given
system of preferential treatment a. Even with
the assumption that all individuals have the
same subjective preference (or utility func-
tion), persons of different earning abilities
may have different indifference maps as defined on Figure 4. (This is similar to James
Mirrlees' model of optimal income taxation.
See J. K. Seade, 1977, for a diagrammatical
illustration.) Given some mild assumptions,
income varies positively and continuously
with earning ability (Mirrlees, 1971). Geometrically, a person with higher earning ability has a flatter indifference curve at a given
point. This is so since a person of lower
earning ability needs to work more to earn a
given income. The equilibrium points
(E1, E2,E3) of three individuals under alternative A are depicted in Figure 4.
Now let us dismantle the system of preferential treatment a. This will make the rich
better off and may make the poor worse off.
If system a is so inefficient such that its
dismantling makes everyone better off, we
have a stronger case for its removal. Thus, let
us take the case where the poor will be made
worse off by its removal. Since the preferential treatment is assumed perfect, there exists
an intermediate income level (say C2) at
which the individual would stay indifferent
by the removal of system a. This individual
must exist in a model of a continuous distribution of individuals but may not exist in
the discrete case. But the actual existence of
this individual is of no consequence to my
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1047
NG: Q UASI-PA RETO SOCIA L IMPRO VEMENTS
argument. After the removal of system a, the
new indifference curve of this individual that
corresponds to the same level of utility as I2
must still pass through the point E2. On the
other hand, individual 3 who is made better
off by the removal of system a, must have a
new indifference curve (IE), that corresponds
to the same level of utility as I3, passing
through a lower point E'. With no preferential treatment against him, he now only needs
a lower level of post-tax income to attain the
original utility level at the same level (0C3)
of pre-tax income.10 Conversely, the new
indifference curve (1) for individual 1 passes
through a higher point E'. Tracing through
all points such as E', E2, E', we arrive at the
new tax schedule /8. With the usual continuity assumptions, this schedule will also be
continuous and smooth. (Continuity and
smoothness are not really necessary for my
central proposition but they make the illustration easier and enable it to be put in terms
of the familiar tangency condition for maximization.) Let us call the tax schedule /3 with
no preferential treatment alternative B. If
the government can collect at least as much
revenue as before to maintain public expenditure, it is clear that everyone will remain at least as well off as under alternative
A. This is so since each person can always
choose to earn the same amount of pre-tax
income and attain the same level of utility as
before. However, if alternative B has greater
disincentive effects, many individuals may
choose to earn less and government revenue
may be smaller than before. Let us examine
this possibility.
Consider Figure 5 which is an enlargement
of the relevant section of Figure 4. If the new
indifference curve of individual 2 does not
only pass through E2 but also stays un10This is obviously true with the assumption of given
earning abilities. With the relaxation of this assumption,
it may be thought that I3 may pass above E3 (and I,
below El) if the wage rate of individual 3 (individual 1)
is sufficiently increased (reduced) by the operation of
preferential system a. If this is so, it means that preferential system a in fact favors the rich rather than the
poor when its full effects (including the indirect effect on
earning abilities) are taken into account. This possibility
may thus be disregarded. It is also clear that the indirect
effect is unlikely to outweigh the direct effect.
Post-tax
income
o
C2
Pre-tax
income
C2+
FIGuRE
5
changed at I2 (at least in the neighborhood
of E2), the new tax schedule ,/, being flatter
than a, must cut this indifference curve (I2)'
Individual 2 would then choose to earn a
lower level of pre-tax income, say, at point
F. However, the actual new indifference curve
(1) must be flatter than the old one 12 at
point E2. With no preferential treatment, he
would need less (more) post-tax income if he
were to earn a higher (lower) level of pre-tax
income. (Otherwise /3 would not be flatter
than a to begin with.) Moreover, it can be
shown that I' must be tangential to /3 at E2.
The tax schedule a touches the (highest)
indifference curve I2' Both 12 and a are
reduced in slope to become 1 and /3, respectively. Moreover, the reduction in slope must
be the same at the point E2. Hence /3touches
I' at F2. To see this more clearly, consider a
slightly higher level of pre-tax income C2 + ?.
The slope of '2 at E2 (denoted S2) may be
approximated by GH/E2H. This approximation will become exact equality as we make approach zero, given smoothness in the curve.
Similarly, the slope of 1 at E2 (denoted
S') = JH/E2H, and the slope of a at E2,
S, = KH/E2H, and the slope of /3 at E2,
S# = LH/E2H. Since the denominators of all
these slopes are the same, we may concentrate on the numerators. Slope S2 is larger
than S' by (approximately) GJ, ignoring the
denominator. GJ measures the extent to
which individual 2 would be made better off
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1048
THE AMERICAN ECONOMIC RE VIEW
by the removal of preferential system a had
he chosen to earn C2+ - instead of C2.11
Slope Sa is larger than S8 by KL. Thus KL
measures the extent to which the individual
who actually earned C2+ - under alternative
A would be made better off by the removal
of preferential system a if he were to keep
earning C2 + e. It must be recognized that
GJ need not equal KL. Although the pre-tax
(C2 + c) incomes of both individuals are the
same if the above hypothetical conditions
prevail, they have different earning abilities.
The same pre-tax income must then imply
different hours or intensities of work. This
difference in hours of work may then make
them willing to forgo a different sum of
post-tax income to remove the same system
(and the same degree) of preferential treatment. However, as we make - approach zero,
not only do the above approximate measures
of slopes become exact, the difference in the
earning abilities of the two individuals also
approaches zero. Given continuity, the
amount by which S2 is larger than S2' will
than be equal to the amount by which Sa is
larger than S, at point E2 as the measures of
these slopes are made exact. Since S2 = Sa at
E2, so SS2-= at E2. It is then not difficult to
see that, under alternative B, not only can
individual 2 attain the same level of utility as
before by earning the same income as before,
he has no incentive to earn a different income. Given some convexity assumptions, he
would be positively worse off if he operated
at a different point.
Let us now go back to Figure 4 to consider
the position of individual 3. Now S3 (slope of
I' at E') may differ from S3 for two reasons.
One is the same as that which makes S2
differ from S2, that is, the removal of preferential treatment tends to make the slope
flatter. But since E3 and E' are now two
1l This is so due to the argument in Section III
abstracting away the possible second-best effect of preferential system a. This effect may change the tradeoff
between consumption and leisure, i.e., the slopes of
indifference curves in the figure. Then GJ may partly
reflect this second-best effect. However, this second-best
effect may go in either direction and, as argued above,
would result in a negative expected gain. Thus, by
abstracting away the second-best effect, we in fact give
alternative A an advantage.
DECEMBER 1984
different points, there is an additional reason
for S3 differing from S3. The difference in
post-tax income may make the individual
have a different tradeoff between consumption (or post-tax income) and leisure (related
to pre-tax income). However, SA (at E') also
differs from Sa (at E3) for these two reasons.
It is thus not difficult to see that S must
equal S3' at E3. Individual 3 will choose to
earn the same amount of pre-tax income as
before. Similar reasoning shows that under
alternative B, all individuals will choose to
earn the same amounts of pre-tax income as
under alternative A. Alternative B thus provides the same degree of incentives and the
same degree of equality in the distribution of
real income (utility) as alternative A.
Even if all individuals earn the same
amount of pre-tax income, can we be sure
that government revenue is no smaller under
alternative B? In Figure 4, let C1 (it could be
zero) be the lowest pre-tax income earned
and C3 be the highest. The change in government revenue in moving from alternative A
to B equals the area E2E3E weighted by
population density function along the horizontal axis minus the area E' E1E2, similarly
weighted. It is clear that the weighted area
F2F3 E' must be larger than the weighted
area E'EIE2. The former measures the aggregate amount by which all individuals
earning more than C2 are made worse off by
preferential system a. The latter area measures the aggregate amount by which all
individuals earning less than C2 are made
better off by system a. If the former area was
smaller than the latter, system a would be
justified on pure efficiency grounds to start
with. Thus if system a is truly preferential,
the former area must be larger than the
latter. For example, the use of unequal income weighting in cost-benefit analysis may
sanction projects with positive unweighted
aggregate net benefits. But such projects will
be sanctioned without the use of unequal
income weighting and would be undertaken
under alternative B, too. Hence the difference in tax schedules a and /3 is caused
by the effects of preferential measures such
as unequal income weighting when they are
effective in sanctioning projects with negative
unweighted aggregate net benefits.
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VOL. 74 NO. S
NG: Q UASI-PA RETO SOCIA L IMPRO VEMENTS
From the above discussion, it can be seen
that alternative B not only provides the same
degree of incentives and the same degree of
equality in the distribution of real income
(utility), it also generates more government
revenue than alternative A. This extra amount
of revenue is a measure of the superiority of
B (no preferential treatment but more progressive income taxation) and can be used to
make everyone better off by increasing public expenditure and/or lowering taxes all
round.
The argument above is based on the assumption of perfect preferential treatment.
The degree of preferential treatment is taken
to be a monotonically decreasing function of
incomes across all individuals. In practice,
preferential treatment in government expenditure cannot be perfect. For one thing,
some expenditures benefit all people in the
same geographical area. The government may
choose to spend more on poor areas, but a
rich person living in a predominantly poor
area will benefit as well. A person is not
likely to change his place of residence each
time his income is increased. Hence, for any
person living in a particular area, he will not
be appreciably adversely affected if he earns
more by those government expenditures that
are geographically specific. The increase in
his income does not appreciably increase the
average income of the whole area. But for
the purpose of income taxation, it is individual income alone that counts and not the
average income of the whole area. It follows
that the disincentive effect of pure income
taxation (alternative B) is greater than that
of income taxation with lower progressivity
but with imperfect preferential treatment (alternative A'). Does it follow that alternative
B is inferior to alternative A'? No, as the
following paragraph shows.
The reason we have to make do with imperfect preferential treatment is the infeasibility or very high costs of effecting perfect
preferential treatment, not that we prefer
imperfect preferential treatment (alternative
A') to perfect preferential treatment (alternative A) as such. Abstracting from the problems of feasibility and transaction costs, alternative A is preferable to A'. But it has
been argued above that alternative B is pref-
1049
erable to alternative A (without counting the
transaction costs involved in A). It follows
that alternative B must be preferable to A'.
This is so despite the fact that the disincentive effect is higher under B. The imperfection of alternative A' involves welfare loss in
terms of inequity which must be larger than
the costs of higher disincentive effects of B
or A (which have the same incentives), otherwise A' would be preferable to A. Thus the
problem of imperfection in preferential treatment does not affect my conclusion.
REFERENCES
Atkinson, Anthony B. and Stiglitz, Joseph E.,
" The Design of Tax Structure: Direct
versus Indirect Taxation," Journal of Public Economics, July-August 1976, 6, 55-75.
Baumol, William J. and Fischer,Dietrich,"The
Output Distribution Frontier: Alternatives
to Income Taxes and Transfers for Strong
Equality Goals," American Economic Review, September 1979, 69, 514-25.
Bergstrom,TheodoreC. and Cornes,RichardC.,
" Independence of Allocative Efficiency
from Distribution in the Theory of Public
Goods," Econometrica, November 1983,
51, 753-66.
Boadway,RobinW., "The Welfare Foundation
of Cost-Benefit Analysis," Economic Journal, December 1974, 84, 926-39.
Bos, Dieter, "Income Taxation, Public Sector
Pricing, and Redistribution," typescript,
1984.
Buchanan,James M. and Tullock,Gordon,The
Calculus of Consent, Ann Arbor: University of Michigan Press, 1962.
Chipman,John S. and Moore, James C., "The
New Welfare Economics 1939-1974," International Economic Review, October
1978, 19, 547-84.
Corden, W. M., Trade Policy and Economic
Welfare, London: Oxford University Press,
1974.
Dodgson,J. S., "Consumer Surplus and Compensation Tests," Public Finance, No. 3,
1977, 32, 312-20.
Feldstein, Martin S., "Distributional Preferences in Public Expenditure Analysis," in
H. M. Hochman and G. E. Patterson, eds.,
Redistribution ThroughPublic Choice, New
This content downloaded from 155.69.24.171 on Fri, 30 Jan 2015 02:41:33 AM
All use subject to JSTOR Terms and Conditions
1050
THE AMERICAN ECONOMIC REVIEW
York: Columbia University Press, 1974.
Gorman,W. M., "The Intransitivity of Certain
Criteria used in Welfare Economics," Oxford Economic Papers, February 1955, 7,
25-35.
Harberger,A. C., "The Three Basic Postulates
for Applied Welfare Economics: An Interpretive Essay," Journal of Economic Literature, September 1971, 9, 785-97.
_
, "On the Use of Distributional
Weights in Social Cost-Benefit Analysis,"
Journal of Political Economy, April 1978,
86, S87-S120.
Hicks, John R., "The Valuation of Social Income," Economica, May 1940, 7, 105-24.
___
"The Rehabilitation of Consumer's
Surplus," Review of Economic Studies,
February 1941, 8, 108-16.
Hirshleifer,Jack, de Haven, J. C. and Millman,
J. W., Water Supply: Economic Technology,
and Policy, Chicago: University of Chicago
Press, 1960, rev. 1969.
Hotelling, Harold, "The General Welfare in
Relation to Problems of Taxation and of
Railway and Utility Rates," Econometrica,
July 1938, 6, 242-69.
Kaldor, Nicholas, " Welfare Propositions of
Economics and Interpersonal Comparison
of Utility," Economic Journal, September
1939, 49, 549-52.
Kemp,MurrayC. and Ng, Yew-Kwang,"On the
Existence of Social Welfare Functions, Social Orderings and Social Decision Functions," Economica, February 1976, 43,
59-66.
, "More on Social Welfare
and
Functions: The Incompatibility of Individualism and Ordinalism," Economica,
February 1977, 44, 89-90.
and _
, "The fncompatibility of
Individualism and Ordinalism," Mathematical Social Sciences, July 1982, 3,
33-38.
Leibenstein, Harvey, "Long-Run Welfare
Criteria," in J. Margolis, ed., The Public
Economy of Urban Communities, Baltimore: Johns Hopkins University Press,
1965.
Little, I. M. D., A Critiqueof WelfareEconomics, London: Oxford University Press,
1950; 1957.
DECEMBER 1984
Mirrlees, James A., "An Exploration in the
Theory of Optimal Income Taxation," Review of Economic Studies April 1971, 38,
175-208.
, " Optimal Tax Theory: A Synthesis,"
Journal of Public Economics, November
1976, 6, 327-58.
,_
The Theory of Optimal Taxation,"
in K. J. Arrow and M. D. Intriligator, eds.,
Handbook of Mathematical Economics, Vol.
III, Amsterdam: North-Holland, 1981.
Mishan, Ezra J., Welfare Economics: An Assessment, Amsterdam: North-Holland,
1969.
Musgrave,RichardA., "Cost-Benefit Analysis
and the Theory of Public Finance," Journal of Economic Literature, September
1969, 7, 797-806.
Ng, Yew-Kwang,"Bentham or Bergson? Finite
Sensibility, Utility Functions, and Social
Welfare Functions," Review of Economic
Studies, October 1975, 42, 545-70.
,_
"Towards a Theory of Third Best,"
Public Finance, No. 1, 1977, 32, 1-15.
Welfare Economics: Introductionand
Development of Basic Concepts, London:
Macmillan, 1979; 1983.
, "Beyond Pareto Optimality: The
Necessity of Interpersonal Cardinal Utilities in Distributional Judgements and Social Choice," Zeitschriftfur Nationalokonomie, November 1982, 42, 207-33.
Polinsky, A. Mitchell, "Probabilistic Compensation Criteria," Quarterly Journal of
Economics, August 1972, 86, 407-25.
Sandmo, Agnar, "Optimal Taxation: An Introduction to the Literature," Journal of
Public Economics, June 1976, 6, 37-54.
Scitovsky,Tibor,"A Note on Welfare Propositions in Economics," Review of Economic
Studies, November 1941, 6, 77-88.
Seade, J. K., "On the Shape of Optimal Tax
Schedules," Journal of Public Economics,
April 1977, 7, 203-35.
Skolnik, M. L., "A Comment on Professor
Musgrave's Separation of Distribution
from Allocation," Journal of Economic
Literature, June 1970, 8, 440-42.
Suzumura,Kotaro, "On Distributional Value
Judgments and Piecemeal Welfare Criteria," Economica, May 1980, 47, 125-39.
This content downloaded from 155.69.24.171 on Fri, 30 Jan 2015 02:41:33 AM
All use subject to JSTOR Terms and Conditions